An analysis of HDG methods for the vorticity-velocity-pressure formulation of the Stokes problem in three dimensions

Abstract

We provide the first a priori error analysis of a hybridizable discontinuous Galerkin (HDG) method for solving the vorticity-velocity-pressure formulation of the three-dimensional Stokes equations of incompressible fluid flow. By using a projection-based approach, we prove that, when all the unknowns use polynomials of degree $k\ge 0$, the $L^2$-norm of the errors in the approximate vorticity and pressure converge to zero with order $k+1/2$, whereas the error in the approximate velocity converges with order $k+1$.